Generalized quasiminimality conjecture for countably many elliptic exponentials

Let $\exp$ denote complex exponentiation, and let $\{E_i\}$ be any countable set of complex elliptic curves, with associated maps $\exp_{E_i}$. Generalized quasiminimality conjecture. The complex field expanded by exponentiation and the maps $\exp_{E_i}$ for any countable set of complex elliptic curves is quasiminimal. The source states that this conjecture would imply the preceding quasiminimality conjectures for elliptic exponential reducts, but gives no proof or resolution.